Re: EllipticTheta error message

• To: mathgroup at smc.vnet.net
• Subject: [mg39936] Re: [mg39907] EllipticTheta error message
• From: Dr Bob <drbob at bigfoot.com>
• Date: Wed, 12 Mar 2003 02:31:22 -0500 (EST)
• References: <200303110736.CAA08670@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Version 4.2.1 under WinXP does the same thing.

I think the problem is that the calculation encounters terms like

EllipticThetaPrime'[3,1,0.904837]
EllipticThetaPrime''[3,1,0.904837]
EllipticThetaPrime'''[3,1,0.904837]

You need to differentiate WRT the second argument, and Mathematica has
somehow forgotten that.

EllipticThetaPrime is the derivative with respect to that same second
argument of EllipticTheta.  Perhaps a fix would be to define the above
expressions.  For instance,

Derivative[n_][EllipticThetaPrime][a_, b_, c_] := Block[{bb},
D[EllipticThetaPrime[a, bb, c], {bb, n}] /. bb -> b]
Derivative[k_Integer][Derivative[0, n_Integer, 0][EllipticThetaPrime]][
a_, b_, c_] := Block[{
bb}, D[EllipticThetaPrime[a, bb, c], {bb, k + n}] /. bb -> b]

That doesn't eliminate the error message, but together with the following,
it does:

f[x_] = EllipticTheta[3, x, 1/E^(0.1)]^2/10
Series[f@x, {x, 1, 4}]

Maybe that's the right answer; I don't know.

What we might need is to make Mathematica forget the EllipticThetaPrime
function.  Something like this:

D[EllipticTheta[a_, b_, c_], b_] =.

But that fails.  I'm not sure what has to be unprotected to make that work.

Bobby

On Tue, 11 Mar 2003 02:36:43 -0500 (EST), Enrique Zeleny
<ezeleny at fismat1.fcfm.buap.mx> wrote:

>
> Version 4.1 on Linux gives a spurious error message
>
>
> In[1]:= Series[EllipticTheta[3, x, 1/E^(1/10000000000)]^2/
> 10000000000, {x, 1, 4}]
>
> EllipticThetaPrime::argr:
> EllipticThetaPrime called with 1 argument; 3 arguments are expected.
>
> All EllipticThetaPrime in the result have the correct number of arguments
>
>
> Enrique Zeleny
> UAP, Mexico
>
>
>

--
majort at cox-internet.com
Bobby R. Treat

```

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